It seems I do have very dirty electricity. My first attempt to address the problem was to install the recommended dedicated line. But first we rigged up a test dedicated line. There was no reduction in noise.
Yes, this exactly. I don't know why people are enamored with plugging their amps directly into the wall and into a dedicated line, as if that solves anything.
The only thing you get is a reduction in noise from other components on the same line, but not a complete elimination of both household and outside noises.
In addition, the dedicated line is only relatively more voltage stable. Relatively meaning if you plug a vacuum into the same circuit you'll get a bigger sag than if you plug it somewhere else, but at the end of the day you are still subject to seasonal and hour to hour variations due to HVAC, ovens, hair dryers, etc., and of course surges.